Asymptotic Results for Configuration Model Random Graphs with Arbitrary Degree Distributions (2010)

09/27/2010 at 10:38 pm

Luke Fostvedt, Dan Nordman, Alyson Wilson

Abstract: We consider a model for generating a random graph using the configuration model. In the configuration model, each node draws a degree independently from a marginal degreed distribution and endpoints pair randomly. We establish non-trivial bounds on the expected sizes of “buckets ” for large graphs. We define nodes i and j in a graph as neighbors if they share an edge, and we define the “bucket ” associated with node i as the set of nodes that are its neighbors and have degree greater than node i. We formalize this argument by providing an analysis for the expected number of items and pairs in a “bucket ” for arbitrarily specified degree distributions, which include power laws.

Paper: Technical Report

Fixed-cost vs. Fixed-risk post-election audits in Iowa

09/12/2010 at 10:31 pm

Jonathan Hobbs, Luke Fostvedt, Adam Pintar, David Rockoff, Eunice Kim, and Randy Griffiths

Electoral integrity has been a forefront issue during the past decade. Policy developments such as voter-verified paper records and post-election audits bolster transparency and voter confidence.

paper: pdf

JSM 2010: An Example of Performance Analysis for Network Community Detection

08/02/2010 at 9:08 pm

Abstract: Community detection algorithms have many applications ranging from search engines on the world wide web to the detection terrorist networks. While the computer scientists are trying to detect “clumpiness” in networks, as statisticians we are analyzing the performance of the algorithm. We pick a node and determine its expected number of neighbors with a degree greater than or equal to this chosen node. This is colloquially referred to the number of nodes in the chosen node’s “bucket”. We show that, for a multigraph with an arbitrary node degree distribution, both the number of nodes in the bucket and the number of pairs of nodes in the bucket are asymptotically finite. This is in contrast to an Erdos Renyi random graph where this quantity increases with O(n).

Poster: JSM 2010 Poster

Measure Theory and Probability Theory Study Guide

12/29/2009 at 9:24 am

Study Guide compiled by Cory Lanker and Luke Fostvedt, Iowa State University
Content includes: Sigma Algebras, Measurable Sets, Lebesgue Measures, Lebesgue Integration, General Lebesgue Integrals, Product Measures, Radon-Nikodym Theorem, Fubini and Tonelli’s theorems, Lebesgue Fundamental Theorem of Calculus, Inequalities, Independence, Borel-Cantelli Lemmas, Law of Large Numbers, Convergence in Probability, Convergence is Distribution, Kolmogorov Theorems, Continuous Mapping Theorem, Tightness, and Method of Moments.

Source: class notes by Dan Nordman, Fall 2009, STAT642, and “Real Analysis” by H. Royden and “Measure Theory” by P.R. Halmos. All references in this document are to Professor Dan Nordman’s class notes.
Content: This study guide is a good supplement to the Athreya Lahiri Text.

Study Guide: Measure Theory and Probability Theory Study Guide

Post Election Audits in Iowa

09/12/2009 at 10:17 pm

Abstract: During the summer of 2008, several statisticians in Iowa learned of developing post-election audit legislation for the state, a collective effort of state legislators, county auditors and active citizens. Since then, faculty and students at three Iowa universities have worked with audit advocates around the state and election audit experts from around the country to promote risk-limiting audit legislation in Iowa. The input from a number of statisticians with experience and expertise in post-election audits has helped shape our strategy, which is focused on developing a dialogue between statisticians and election officials. Our initial contacts with local officials have underscored the critical importance of communication in promoting risk-limiting audits. Our efforts in 2009 will include additional student involvement and exploring pilot audits for Iowa’s next general election.

Slides: Post Election Audits Presentation